Explicitly-Adaptive Time Delay Estimation for Wide-Band Signals

Time delay estimation is a very important operation in ultrasound time-domain flow mapping and correction of phase aberration of an array transducer. As the interest increases in the application of one and a half-dimensional (1.5-D) and two-dimensional (2-D) array transducers to improving image quality and three-dimensional (3-D) imaging, the need of simple, fast, and sufficiently accurate algorithms for real-time time delay estimation becomes exceedingly crucial. In this paper, we present an adaptive time-delay estimation algorithm which minimizes the problem of noise sensitivity associated with the one bit correlation while retaining simplicity in implementation. This algorithm converts each sample datum into a two bit representation including the sign of the sample and an adaptively selected threshold. A bit pattern correlation operation is applied to find the time delay between two engaged signals. By using the criterion of misregistration as an indicator, we are able to show that the proposed algorithm is better than one bit correlation in susceptibility to noise level. Analytical results show that the improvement in reducing misregistration of the two bit correlation over its counterpart is consistent over a wide range of noise level. This is achieved by an adaptive adjustment of the threshold to accommodate signal corruption due to noise. The analytical results are corroborated by results from simulating the blood as a random distribution of red blood cells. Finally, we also present a memory-based architecture to implement the two bit correlation algorithm whose computation time does not depend upon the time delay of the signals to be correlated.

Hyperbolic localization of incipient tip vortex cavitation in marine propeller using spectral kurtosis

High-frequency (HF) communication is critical for applications such as over-the-horizon positioning and ionospheric detection. However, precise time-delay estimation in complex HF channels faces significant challenges from multipath fading, Doppler shifts, and noise. This paper proposes a Modulation Signal-based Adaptive Time-Delay Estimation (MATE) algorithm, which effectively decouples carrier and modulation signals and integrates phase-locked loop (PLL) and delay-locked loop (DLL) techniques. By leveraging the autocorrelation properties of 8PSK (Eight-Phase Shift Keying) signals, MATE compensates for carrier frequency deviations and mitigates multipath interference. Simulation results based on the Watterson channel model demonstrate that MATE achieves an average time-delay estimation error of approximately 0.01 ms with a standard deviation of approximately 0.01 ms, representing a 94.12% reduction in mean error and a 96.43% reduction in standard deviation compared to the traditional Generalized Cross-Correlation (GCC) method. Validation with actual measurement data further confirms the robustness of MATE against channel variations. MATE offers a high-precision, low-complexity solution for HF time-delay estimation, significantly benefiting applications in HF communication systems. This advancement is particularly valuable for enhancing the accuracy and reliability of time-of-arrival (TOA) detection in HF-based sensor networks and remote sensing systems.

Inter-sensor Time Delay Estimation (TDE) can be obtained using Generalized Cross-correlator (GCC), Phase Transform (PHAT) and Hilbert Transform of the cross-correlator. The accuracy of the estimate is affected by signal reflections generated due to the multipath structure of the channel. In this paper, a novel cepstrum based algorithm is proposed for estimating the Time Difference of Arrival (TDOA) across a pair of sensors in multipath environment. The proposed algorithm uses the concept of echo arrival time estimation. It computes the sum of the received signal at two omnidirectional hydrophones and then calculates its power cepstrum. The power cepstrum of the addition of two signals, is termed as the “additive cepstrum”. By addition of the two hydrophone signals in time domain, a virtual echo is generated and the additive cepstrum shows peaks at intervals corresponding to the magnitude of time delay between the two signals and its integer multiples. The algorithm then computes the power cepstrum of the difference of the signals received at the two hydrophones. It is called as the “difference cepstrum”. The difference cepstrum is subtracted from the additive cepstrum and the result is called as the “residual cepstrum”. The residual cepstrum shows peaks at the inter-sensor time delay value and its odd multiples plus the multiplicative noise. The inter-sensor time delay is estimated using a peak detection algorithm. The algorithm gives the absolute time difference of arrival for the sensor pair. Hence, the sign of the time delay is obtained using a further step involving the cross-correlation function in a preceding stage. The time delay estimation algorithm has been implemented for bandlimited white Gaussian noise as source signal and background noise, for various levels of Signal to Noise Ratio (SNR). The performance has been compared with the GCC and PHAT algorithms using standard performance measures and found to be more accurate in terms of reduced percentage of anomalies and reduced MSE of the non-anomalous estimates.

A computationally efficient algorithm for estimating time delay between signals received at two spatially separated sensors is proposed. The delay estimate is adapted directly to maximise the mean product of the first sensor output and the filtered output of the second received signal. The convergence behaviour and variance of the delay estimate are derived. It is shown that the proposed algorithm outperforms the explicit time delay estimator at a low signal-to-noise ratio.

Positioning systems based on the Time Difference of Arrival (TDOA) often struggle to accurately estimate time delays for partial discharge signals in complex electromagnetic environments. To address this, we introduce an improved joint-weighted generalized cross-correlation (GCC) time delay estimation algorithm. Traditional GCC time delay estimations, when reliant on conventional weighted functions, significantly underperform in situations characterized by low signal–noise ratios (SNRs). Our proposed improved joint weighted function combines the advantages of both phase transform (PHAT) and correlation transform (SCOT) weightings, resulting in a composite function. Compared to the conventional weighted GCC, the improved joint weighted GCC displays a more distinct peak in cross-correlation functions and ensures more robust delay estimations, especially under low SNR conditions. Experimental results indicate that the improved joint-weighted GCC algorithm achieves an error margin below 1 ns in challenging outdoor electromagnetic scenarios, demonstrating its aptitude for detecting and localizing partial discharge signals in practical engineering applications.

We present a novel maximum-likelihood (ML) algorithm for joint delay estimation and frame synchronization. The algorithm operates on coded signals and exploits the code properties by accepting soft information from the MAP decoder. Issues of convergence are addressed and we show how computational complexity may be reduced without any performance degradation. Simulation results are presented for convolutional and turbo codes, and are compared to performance results of conventional algorithms both in terms of mean square estimation error (MSEE) and BER. We show that code-aided delay estimation always improves the MSEE, but not necessarily the BER. On the other hand, code-aided frame synchronization is mandatory, in order to avoid either significant BER degradations or the need for very long pilot sequences.Key wordsturbo synchronizationdelay estimationframe synchronizationEM algorithm

Pre-distortion algorithms for the compensation of AM/AM and AM/PM non-linearities of high power amplifiers (HPA) require a previous estimation of the delay introduced by the analog chains at the input and output of the amplifier. This paper presents a coarse time delay estimation (TDE) algorithm to within one-sample resolution based on a conditional entropy principle. The delay estimate is computed via one dimensional search on the proposed TDE spectrum.

Time delay estimation is the basis of the localization algorithm for partial discharge (PD) based on time difference in GIS, and it is the key to the accuracy of localization. In this paper, the theory of fractional Hilbert transform for time delay estimation is described. Based on fractional Hilbert transform, a method for estimating the time delay of GIS ultra high frequency partial discharge is proposed, and the numerical implementation steps of the algorithm are given. According to the abnormal partial discharge signals found in the switch gate during the inspection of certain 220kV GIS equipment, high frequency electromagnetic wave is collected by the high speed oscilloscope. According to the time delay of the signal, the space position of the partial discharge source is located from the the disk type insulator pouring hole 1.25 meters. After the disintegration of the switch air chamber, the distance between the discharge source and the pouring hole is 1.3 meters. The error of the partial discharge source localization based on fractional Hilbert algorithm is significantly lower than that of the bi-spectrum and the frequency domain time delay estimation algorithm.

The paper discusses the implementation of correlation algorithm for time delay estimation on a Raspberry Pi single-board computer. The implemented correlation algorithm is based on Fourier transform. In the course of the study, we applied two alternative solutions for the software implementation of discrete Fourier transform. The first solution stands on FFTW library and uses general-purpose quad-core ARM Cortex A53 processing unit. The alternative method uses VideoCore IV graphic processing unit and is implemented via firmware GPU_FFT library. We have performed a computational experiment on a Raspberry Pi 3B to determine which solution is more preferable for the implementation of correlator. After a comparative study we figured out that estimated processing time is highly dependent on computations parameters and input signals. For small FFT window sizes CPU is proved to be a preferable option. However, for large FFT windows GPU allows significantly accelerating the computations. At some point, you can achieve even better performance by using batching and GPU for direct FFT and CPU for inverse FFT. According with the results, we have concluded that both alternatives have their own potential advantages and particular drawback. We also establish, that Raspberry Pi 3 B computer with HiFiberry extension can be used as a real-time correlator for audio signals.

The Fair Weighting Based IRWLS Algorithm For Time Delay Estimation In Underwater Target Tracking

SummaryThe near‐field electromagnetic ranging systems exploit the near‐field phase behavior of low frequency signals for indoor real‐time ranging. Conventionally, phase detector is used to determine the phase of electric and magnetic fields. Subsequently, the phase difference is used to estimate a distance value. In adaptive time delay estimation approach, the time delay between electric and magnetic signals is used instead of phase difference for an estimation. This method does not require a priori knowledge of the transmitting signals and can obtain better performance in low signal‐to‐noise ratio environment. In this paper, we propose a digital near‐field electromagnetic ranging system design and implement it on field‐programmable gate array. This system is composed of time delay estimator, frequency estimator, and received signal strength indicator. A maximum correntropy criterion–based explicit time delay estimation algorithm with a delay in the coefficient update is implemented to estimate the time delay in real time. The fast Fourier transform and received signal strength indicator modules determine the signal frequency and the signal strength received, respectively. Our experimental results indicate that the delayed maximum correntropy criterion–based explicit time delay estimation algorithm has fast convergence rate and good steady‐state performance in an impulsive noise environment.

In this article, a modified fractional internal model control (IMC) filter structure is proposed to design a fractional filter Proportional-Integral-Derivative (FFPID) controller for improved disturbance rejection of second order plus time delay (SOPTD) processes. The proposed method aims at improving the disturbance rejection of slow chemical processes as the tuning rules for such processes are limited. The present design also considers the higher order approximation for time delay as it gives improved response for higher order processes. There is an additional tuning parameter in the proposed IMC filter apart from the conventional IMC filter time constant, which is tuned according to the derived formula. The additional adjustable parameter achieves the disturbance rejection and the closed loop stability. The simulation results have been performed for the same degree of robustness (maximum sensitivity, Ms) for a fair comparison. The results show an improved disturbance rejection for lag dominant and delay significant SOPTD processes with the proposed controllers designed using higher order Pade’s approximation of time delay than the proposed method using first order approximation and the conventional method. The closed loop robust performance is observed for perturbations in the process parameters and the performance is also observed for noise in the measurement. The robust stability analysis is carried out using sensitivity functions. In addition, the Ms range is also identified over which the system gives robust performance for the controllers designed using higher order pade’s approximation of time delay compared to conventional method.

By exploiting cyclostationarity of received signals at certain cycle frequency, i.e., evaluating the cyclic correlation or cyclic spectrum of the received signals at certain cycle frequency, the signal-selective time-difference-of-arrival (TDOA) estimation algorithms which based on cyclic statistics are highly tolerant to the interference and Gaussian noise. However, conventional cyclostationary TDOA methods based on the second-order cyclic correlation function or cyclic spectrum will degenerate severely in impulsive noise. In this paper, a new time delay estimation algorithm based on the fractional lower-order statistics (FLOS) and cyclostationarity is proposed for communications signals under non-Gaussian alpha stable distribution impulsive noise. Simulation results show that the proposed method is efficient and stable, and it outperforms the cyclostationarity based multi-cycle and FLOS based methods under impulsive noise and interference.

The estimation of delay and Doppler shift parameters in the presence of multiple targets in radar applications are addressed in this study. The construction of a new ambiguity function, namely, exponential ambiguity function, is proposed by introducing an exponent $p$ into the traditional ambiguity function. Some important properties of the exponential ambiguity function are derived. Then the joint delay and Doppler shift estimation algorithm is proposed based on the combination of the exponential ambiguity function and wavelet denoising method. The performance of the proposed estimation algorithm is theoretically analyzed, verified via Monte Carlo simulation, and compared with the performance of the traditional ambiguity function. Simulation results and theoretical performance analysis show that the proposed estimation algorithm outperforms the existing methods for closely located targets.